Elliptic curve isogeny class with LMFDB label 86700.x (Cremona label 86700bb)

• Label: 86700.x
• Number of curves: $1$
• Conductor: $86700$
• CM: no
• Rank: $0$

Rank

The elliptic curve 86700.x1 has rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - T + 11 T^{2}\)	1.11.ab
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(19\)	\( 1 - 7 T + 19 T^{2}\)	1.19.ah
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 86700.x do not have complex multiplication.

Modular form 86700.2.a.x

Isogeny graph

Elliptic curves in class 86700.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
86700.x1	86700bb1	\([0, -1, 0, -568270333, -5213879671463]\)	\(5818717724672/59049\)	\(205955750566804500000000\)	\([]\)	\(19094400\)	\(3.6320\)	\(\Gamma_0(N)\)-optimal